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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On Darboux's lemma


Author: Hans Samelson
Journal: Proc. Amer. Math. Soc. 70 (1978), 126-128
MSC: Primary 58A10
MathSciNet review: 0474367
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Abstract: We resurrect Carathéodory's proof of Darboux's lemma (normal form $ \Sigma d{p_i}d{q_i}$ for a nondegenerate closed 2-form). The proof is simple and straightforward (after eliminating unnecessary steps) and deserves to be better known. It involves, not surprisingly, the canonical differential equations of Hamilton-Jacobi theory.


References [Enhancements On Off] (What's this?)

  • [1] C. Carathéodory, Variationsrechnung und partielle Differentialgleichungen erster Ordnung, Teubner, Leipzig, 1935; English edition: Calculus of variations and partial differential equations of first order, Holden-Day, San Francisco, 1965.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0474367-0
PII: S 0002-9939(1978)0474367-0
Article copyright: © Copyright 1978 American Mathematical Society